Atmospheric turbulence is a well-known source of distortion that can degrade the quality of images and videos acquired by cameras viewing scenes from long distances. In astronomy in particular, stars in outer space viewed through ground-based telescopes appear blurry and flickering. The blurring and flickering is due to fluctuation in the refractive index of Earth's atmosphere. The fluctuations in the refractive index of the atmosphere involve many factors including wind velocity, temperature gradients, and elevation. The dominant factor is usually temperature variation.
Light in a narrow spectral band approaching the atmosphere from a distant light source, such as a star, is modelled by a plane wave. The planar nature of the wave remains unchanged as long as the wave propagates through free space, which has a uniform index of refraction. The atmosphere, however, contains a multitude of randomly distributed regions of uniform index of refraction, referred to as turbulent eddies. The index of refraction varies from eddy to eddy. As a result, the light wave that reaches the surface of the Earth is not planar. FIG. 1 demonstrates the effect of Earth's atmosphere on the wavefront of a distance point source. In FIG. 1, after the plane wave passes through a turbulent layer in the atmosphere, the plane wave's wavefront becomes perturbed. Excursions of the wave from a plane are manifested as random aberrations in astronomical imaging systems. The general effects of optical aberrations include broadening of the point spread function and lower resolution. Although some blurring effects can be corrected by fixed optics in the design of the telescope, the spatially random and temporally varying nature of atmospheric turbulence makes correction difficult.
In ground-based long-distance surveillance, the situation is often worse because, unlike astronomical imaging, the effects of turbulence in long-distance surveillance exist in the whole imaging path. Therefore the captured images not only exhibit distortion caused by atmospheric turbulence close to the lens aperture, with similar results to that in astronomy, but also exhibit distortion caused by atmospheric turbulence closer to the object of interest.
The observation of atmospheric turbulence and the impact of atmospheric turbulence on astronomical imaging are long known. In the absence of turbulence correction, attaining diffraction limited performance at visible wavelengths with a ground-based telescope bigger than a few tens of centimetres in diameter was considered impossible. Isaac Newton noted that the point spread function of a telescope looking through turbulence is broader than would be expected in the absence of the atmosphere. However, the turbulence effect could not be recorded in short exposure images referred to as ‘speckle images’ until fast film systems were developed.
In order to efficiently correct for the effect of atmospheric turbulence, accurate estimation of the strength of turbulence in long distance imaging is important. The turbulence strength Cn2 depends on many factors such as the average shear rate of the wind and the average vertical gradient of the potential temperature.
Because the average shear rate of the wind and the average vertical gradient of the potential temperature are typically difficult to measure, in practice, the turbulence strength Cn2 (or equivalently the Fried parameter r0) is often measured using profiling techniques such as SLODAR (SLOpe Detection And Ranging). In Slope Detection And Ranging techniques, two Shack-Hartmann wavefront sensors are used to estimate not only the height of the turbulent atmospheric layer but also the turbulence strength Cn2 for each layer. In Slope Detection And Ranging turbulence profiling, the total turbulence strength along the imaging path is estimated using a temporal variance of the one dimensional motion of the centroids in the Shack-Hartmann image. Using a temporal variance for turbulence profiling requires multiple frames and therefore is not a real-time estimate of turbulence strength. Furthermore, a Shack-Hartmann wavefront sensor requires a point source (guide star) to work properly, which is not always available in long distance imaging along horizontal paths. In addition, Shack-Hartmann wavefront sensors generally have a small working area, making the sensors unsuitable for wide-field applications such as long distance surveillance. Shack-Hartmann wavefront sensors also require specialised optics which significantly raises the cost and size of an imaging system.
Turbulence strength measurement using passive tomography has also been proposed. In the passive tomography method, multiple consumer-grade cameras are set up to capture a short video of the scene from different angles. Around 100 captured frames from each camera are used to estimate the temporal variance σx2 of the image pixel displacement x. Using the relationship between this temporal variance and the turbulence strength along the line of sight of each camera, a linear system can be solved to obtain the 3-dimensional distribution of the turbulence strength Cn2. Although the passive tomography method has an advantage of being wide-field and needing only simple equipment, the method still requires a large number of cameras and complex set-up. Most importantly, because multiple frames are needed to calculate the temporal variance, the result is not a real-time measurement of the turbulence strength.
Additionally, one can also artificially introduce a phase diversity or wavelength diversity in two or more simultaneous captures of the same scene in order to measure the turbulence. In particular, the phase diversity compensation method uses a known additive phase term. For example, a partitioned aperture wavefront (PAW) sensing method uses 4 simultaneous captures with contrived phase steps to calculate the wavefront phase slope in order to correct phase disturbance caused by a sample. In some known implementations, a scene is recorded at two different narrow-band wave lengths centred at λ1 and λ2 and the turbulence optical transfer function (OTF) is estimated using an autocorrelation of a generalized pupil function. Introducing an artificial phase or wavelength diversity involves complex system design and calibration and often limits the application to research fields such as microscopy or special multi-spectral imaging.
While the measurement of turbulence strength is not straightforward, most atmospheric turbulence compensation methods rely on a reasonable estimate of a turbulence strength value. Generally, there are two basic categories to compensate for the effects of atmospheric turbulence, namely, 1) adaptive optics systems, and 2) post-processing atmospheric turbulence compensation systems.
Adaptive optics systems are hardware-based systems that can correct atmospheric-turbulence effects in real-time by directly compensating for the wavefront phase disturbance using a deformable mirror. Adaptive optics systems are generally cumbersome, require extensive hardware and are expensive. Adaptive optics systems are also predominantly designed for fixed sites and are not typically portable.
Post-processing atmospheric turbulence compensation systems are largely implemented in software. One common sub-category of software-based systems is the speckle imaging method, where a large number of fast exposures of the scene are captured and combined to produce a turbulence free image. One example is a tiled bispectral analysis method, where the phase closure property of the bispectrum is utilized to calculate the phase of the spatial frequency spectrum of the original turbulence free scene using overlapping tiles in the captured frames.
Another speckle imaging example is ‘lucky imaging’, where a small number of good quality frames or regions are selected from a large number of mostly highly distorted frames, to restore the high resolution scene. Traditionally, criteria such as variance or gradient are used. However, the selection of good quality frames may be unreliable as the variance and gradient are affected by the intrinsic scene spectrum and the lens optical transfer function, as well as by the atmospheric turbulence. In addition, lucky imaging requires discarding many frames to achieve a restored image, and is therefore often highly inefficient in terms of overall light gathering power, and difficult to use when the scene is changing quickly.
Many post-processing turbulence compensation methods apply multi-frame blind deconvolution to improve the frame resolution based on information from multiple frames. However, due to the lack of real-time, local turbulence strength estimation, the effect of blind deconvolution algorithms is minimal.